Nuprl Lemma : rnonzero_wf
∀[x:ℕ+ ⟶ ℤ]. (rnonzero(x) ∈ ℙ)
Proof
Definitions occuring in Statement :
rnonzero: rnonzero(x),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rnonzero: rnonzero(x),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
exists_wf,
nat_plus_wf,
less_than_wf,
absval_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
natural_numberEquality,
applyEquality,
hypothesisEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
intEquality
Latex:
\mforall{}[x:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}]. (rnonzero(x) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-06_53_50
Last ObjectModification:
2015_12_28-AM-00_31_11
Theory : reals
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